The goal of this work is to apply Multiple Criteria Decision Analysis tools, both theoretical and practical, to analyse, support and possibly enhance composite indexes, in particular those related to sustainability assessment. In this context, the Sustainable Development of Energy, Water and Environment Systems Index represents a paradigmatic example and an emerging reference point, thus it is specifically addressed throughout the work. On the theoretical side, the focus is on the property of "independence", i.e., of evaluating an alternative independently of the others. It is argued that this property can be appealing for an index that is conceived to address, over time, an increasing number of inherently evolving systems. A viable and theoretically grounded approach for devising a version of the index fulfilling independence is proposed. On the practical side, the contribution concerns visual support tools. A well-known projective method is adapted to work with the index, and a new tool with comparable expressive capabilities is proposed. The new representation is more focused on the index, technically simpler, and less sensitive to changes in the input data. The features of the visual tools are illustrated exploiting currently available (partially aggregated) index data. In particular, the new tool is used to illustrate two issues addressed in the scientific literature on the index, namely, the use of scenario analysis as a predictive tool, and the decoupling of energy usage and carbon dioxide emissions.